{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R422",
  "content_hash": null,
  "slug": "iso7-attempt-prior-art-audit",
  "type": "attempt",
  "title": "PatternBoost already gives the exact seven-grid value",
  "summary": "The paper defines the same possibly-flat problem, reports SAT-certified small values, and lists f(7)=10.",
  "relevance": "This records a line of attack on the target problem, including what it establishes and where it stops.",
  "relevance_source": "derived",
  "body": "Section 4.1 of PatternBoost defines \\(f(n)\\) for subsets of \\([n]^2\\) containing no possibly-flat isosceles triangle. It states that SAT solvers find optimal constructions for small \\(n\\), and Figure 11 records\n\\[\nf(4)=6,\\quad f(5)=7,\\quad f(6)=9,\\quad f(7)=10.\n\\]\nThis matches the candidate after translating coordinates by one.\n\nThe same paper discusses asymptotic bounds and attributes the question independently to Wu, Ellenberg and Jain, and possibly Erdős. A 2019 MathOverflow question states the collinear-inclusive version explicitly.\n\nOEIS A271907 has a similar title and gives 12 at grid size 7. Its illustrated construction at size 8 contains equally spaced collinear triples, so the sequence follows the nondegenerate-triangle convention in practice. It cannot be used for the present candidate. Keeping the convention explicit prevents the two exact values from being merged.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "published exact and computational results for possibly-flat isosceles-triangle-free subsets of the 7 by 7 grid",
    "bounds": {
      "grid_side": {
        "min": 7,
        "max": 7
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2411.00566",
      "locator": "François Charton, Jordan S. Ellenberg, Adam Zsolt Wagner, and Geordie Williamson, PatternBoost: Constructions in Mathematics with a Little Help from AI, arXiv:2411.00566, section 4.1, Figure 11, and Appendix A; OEIS A271907; MathOverflow question 325127, checked 2026-07-24"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2411.00566",
    "locator": "François Charton, Jordan S. Ellenberg, Adam Zsolt Wagner, and Geordie Williamson, PatternBoost: Constructions in Mathematics with a Little Help from AI, arXiv:2411.00566, section 4.1, Figure 11, and Appendix A; OEIS A271907; MathOverflow question 325127, checked 2026-07-24"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R423",
      "title": "The exact maximum is I_7=10",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "no-isosceles-grid-7",
      "title": "no isosceles grid 7",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}